I’ve made quite a lot exercises that are abailable at codepen. Some of them were dependent on external API which are now not available at all or have their methods changed.
Should I fix it in order to be prepared for any further examination by the FCC teachers and volunteers?
The source code actually speaks for itself and I would like to go on with back-end challenges.

No one is going to check them until you’re getting into the non-profit work, so it may be a good idea to leave them as-is for now. I would definitely recommend fixing them later, but the APIs may change again in between now and then, so you might as well wait.